Sometimes is a good idea to do your research before setting your mind on a false notion.
Please don’t hesitate to go forth and take your own advice.
Sometimes you need to research the right sources before setting your mind on accepting a false authority.
I've researched this quite a lot with founding era documents. I'll note right off the bat, that the first "natural born" President was Martin Van Buren. He was born in 1782, making him the FIRST President born after the Declaration of Independence. He was elected in 1836, so there was an interval of 60 years in which the term "Natural born citizen" didn't apply to the Presidency.
Why is this relevant? It points out the fact that for 60 years nobody paid any attention to the "natural born citizen" requirement, because all previous Presidents were grandfathered in. During this time, the accurate meaning of the term was distorted by deliberate misrepresentation from William Rawle and others.
At the time William Rawle began his deliberate misrepresentation, most of the people who could challenge him on the issue were already dead. His book (A View of the Constitution) became very popular, and as a result of his book and often repeated misapplied notion that we followed English law in everything, a lot of people became convinced that mere birth on the soil is all that is necessary to be a "natural born citizen."
And for the first sixty years, the point didn't really matter. That's another reason why people forgot the correct meaning.
Why did Rawle deliberately misrepresent the meaning of "natural born citizen"? He was attempting to use the English law rule to assert citizenship for slaves. Rawle was a dedicated abolitionist who filed lawsuits to end slavery and who was also the President of the Pennsylvania abolition society.
Rawle NEEDED and fervently desired that the English law be the rule, so he just wrote that it was. Other British trained lawyers agreed with him, and that's how we got so much confusion on the issue.
But people in a position to KNOW the correct answer,(Delegates who debated the matter) tend to quote Vattel or apply the same principle in their own words.